Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
11024749 | Finite Fields and Their Applications | 2019 | 10 Pages |
Abstract
Let F be a finite field and let G be a finite group. We show that if C is a G-code over F with dimFâ¡(C)â¤3 then C is an abelian group code. Since there exist non-abelian group codes of dimension 4 when charF>2 (see the examples in [1]), we conclude that the smallest dimension of a non-abelian group code over a finite field is 4.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
C. GarcÃa Pillado, S. González, V. Markov, O. Markova, C. MartÃnez,